In many situations it is desirable to convert binary data into an analog signal. A common application is in audio equipment modern source materials such as Compact Disk (CD) Digital Video Disk (DVD), Computer Audio Formats such as MP3, MP4, AAC and OGG all store and read out audio/video (AV) information in digital form. In addition, Digital Signal Processing and most Digital Rights Management encoders deal with Digital Signals. Playback apparatus such as speakers, headphones and many video displays require an analog input. Digital signals, in addition, contain high frequency harmonics which result in distortion and damage to components when directly inputted to an analog component. This had led to a growing demand for inexpensive efficient Digital to analog converters (DAC).
The operation of a Digital to analog converter (DAC) is to convert a fixed point binary value into a physical quantity such as an electric voltage or current. Ideally, the voltage or current from a DAC is characterized by a linear function of the input binary value.
Assume a maximum voltage Vmax and a minimum voltage Vmin can be produced from a certain six bit DAC. One way to scale the voltage between Vmax and Vmin for a six bit DAC is to utilize Vmin as a base voltage and to apply an increment to this voltage ΔV (also termed the increment between voltages) defined as (Vmax−Vmin)/26. The possible range of voltage values for this example include Vmin, Vmin+ΔV, Vmin+2ΔV, Vmin+3ΔV, . . . , Vmin+(26−1) ΔV. This method of voltage scaling does not produce the precise maximum voltage, but if the bit width of the DAC were great enough, the difference between the last discrete voltage in the range and Vmax would be nearly identical.
Regardless of the bit width of the DAC there will always be gaps in the voltages produced as is the case for any discrete range. In practice the hardware DAC is of a fixed length and it is only possible to produce the scale of voltages from the bit width of the DAC. It is advantageous to utilize a method for digital to analog conversion which can produce greater resolution than a hardware DAC can provide.